This project is to develop statistical methods for the analysis of the genetic basis of complex diseases with variable age of onset. For complex diseases, disease susceptibility usually is dictated by the interplay of multiple genes and multiple non-genetic factors such as environmental exposures. In the past few years there are many statistical developments for finding genes linked to complex diseases, for example, linkage disequilibrium mapping and linkage analysis have been used for localizing major susceptibility genes. The major goal of this application is to propose novel methods for population-based association studies that will improve our ability to detect susceptibility alleles for common complex diseases. In particular, they will address the following areas: (1) Studies have suggested that disease genes influence not only the occurrence of the disease, but also the age of onset. Modeling the age of onset is important to understanding the genetic factor of these diseases. Simply treating the disease outcome as affected vs. unaffected may lose information as some unaffected subjects at the time of study may be carriers of a predisposing disease gene. The first goal of this project is to develop statistical models that apply survival analysis methods in population-based designs that incorporate the age of onset of diseases with both genetic markers and environmental risk as covariates. (2) For population-based association studies, the gene effects are often confounded by population stratification. Our proposed methods will be robust to population stratification. (3) By the use of tightly linked markers, particularly single-nucleotide polymorphisms, we will develop new methods that test the association between traits and one or more haplotypes while incorporating the age of onset information and environmental risk factors. The proposed methodology will be implemented as user-friendly software. The documentation, distribution and support of the software will be provided.